ACG 2071
Module 11: Differential Analysis and Product Pricing
Differential Analysis
Costs:
Relevant - estimated costs and revenues that are important in the
decision making process.
Sunk costs – that have been incurred in the past are not relevant to the
decision.
Differential revenue:
Is the amount of increase or decrease in revenue expected from a
course of action as compared with an alternative?
Differential cost:
Is the amount of increase or decrease in cost that is expected from a
course of action as compared with an alternative?
Differential income or loss:
Is the difference between the differential revenue and the differential
costs?
Differential analysis:
It focuses on the effect of alternative courses of action on the relevant
revenues.
Differential Revenue from alternatives
Revenue from Alternative A
Revenue from Alternative B
Differential Revenue
Differential cost of alternatives
Cost of Alternative A
Cost of B
Differential cost
Net differential income or loss from alternatives
Created by: M. Mari
Fall 2007
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ACG 2071
Module 11: Differential Analysis and Product Pricing
Types of Decision-making:
1. Lease or sell: management may have a choice between leasing or
selling a piece of equipment that is no longer needed in the business.
The relevant factors to be considered are the differential revenues and
differential costs associated with the lease or sell decision.
Example 1: A corporation can sell an asset for $200,000 less a 6%
selling commission. An alternative would be to lease the asset for
five years at $40,000 per year less $35,000 in costs over the five
years. Which decision would you make?
Differential Revenue from alternatives
Revenue from selling
Revenue from leasing
Differential Revenue
Differential cost of alternatives
Cost of selling: Commissions 6% of sales price
Cost of leasing: operating costs
Differential cost
Net differential loss from leasing
$200,000
$200,000
$0
$12,000
$35,000
-$23,000
-$23,000
Therefore we should sell the asset and save $23,000 in additional costs.
2. Discontinue a segment or product
When a product or a department, branch, territory, or other
segment of a business is generating losses, management may
consider eliminating the product or segment.
It is often assumed, sometimes in error, that the total income
from operations of a business would be increased if the
operating loss could be eliminated.
Discontinuing the product or segment usually eliminates all of
the product or segment’s variable costs.
However, if the product or segment is a relatively small part of
the business, discontinuing it may not decrease the fixed costs.
If contribution margin > 0 then continue production
Created by: M. Mari
Fall 2007
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ACG 2071
Module 11: Differential Analysis and Product Pricing
Example 3:
Sales
Cost of
goods sold
Variable
Fixed
Total CGS
Gross profit
Operating
expenses
Variable
Fixed
Total
Income
Shampoo
$500,000
Conditioner
$400,000
Lotion
$100,000
Total
$1,000,000
$220,000
$120,000
340,000
160,000
$200,000
$80,000
280,000
$120,000
$60,000
$20,000
80,000
$20,000
$480,000
$220,000
700,000
$300,000
$95,000
$25,000
$120,000
$40,000
$60,000
$20,000
$80,000
$40,000
$25,000
$6,000
$31,000
$(11,000)
$180,000
$51,000
$231,000
$69,000
Should we discontinue the production of Lotion?
Sales
Variable cost of goods sold
Manufacturing margin
Variable operating expenses
Contribution Margin
$100,000
$60,000
$40,000
$25,000
$15,000
Since contribution margin is positive, we continue production of the product.
3. Make or Buy
 The assembly of many parts is often a major element in
manufacturing some products, such as autos.
 The product’s manufacturer may make these parts or they may be
purchased.
 Management uses differential costs to decide whether to make or buy
a part.
 Only variable costs are considered.
 Must have unused capacity in the factory.
Created by: M. Mari
Fall 2007
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ACG 2071
Module 11: Differential Analysis and Product Pricing
Example 5: A factory has unused capacity and is considering the
production of a part for its product. The cost of making a part is direct
materials $80, direct labor $75, variable factory overhead $52 and fixed
factory overhead $68. The cost of purchasing the product is $240 a unit.
Should we make or buy?
Does it have unused capacity? Yes
Total variable costs of production:
Direct materials
Direct labor
Variable factory overhead
Total variable costs
Total cost of purchasing
$80.00
$75.00
$52,00
$202.00
$240.00
Since it is cheaper to produce than buy, we will produce and save $38 per
unit.
4. Replace Equipment
 The usefulness of fixed assets may be reduced long before they are
considered to be worn out.
 Equipment may no longer be efficient for the purposes for which it is
used.
 On the other hand, the equipment may not have reached the point of
complete inadequacy.
 Decisions to replace usable fixed assets should be based on relevant
costs.
 The relevant costs are the future costs of continuing to use the
equipment versus replacement
 The book values of the fixed assets being replaced are sunk costs and
are irrelevant.
Created by: M. Mari
Fall 2007
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ACG 2071
Module 11: Differential Analysis and Product Pricing
Example 7: The business is considering the disposal of a machine with
book value of $100,000 and an estimated remaining live of five years. The
old machine can be sold for $25,000. The new machine has a cost of
$250,000. The new machine would have a life of five years and no residual
value. Analysis indicates that the estimated annual reduction in variable
manufacturing costs from $225,000 with the old machine to $150,000 per
year with the new machine. Should we buy the new machine?
Sales price of old
Cost savings:
Old machine
New machine
Savings per year
X five years
Total savings
Cost of new machine
Differential income
$25,000
$225,000
$150,000
$75,000
X 5 years
$375,000
$400,000
$250,000
$150,000
We should sell the old machine since the savings from the new machine
does outweigh the costs.
5. Process or Sell
 When a product is manufactured, it progresses through various stages
of production.
 Often a product can be sold at an intermediate stage of production, or
it can be processed further and then sold.
 Only process further if the revenue is greater than the total costs of
production.
Example 9: Assume that a business produces kerosene in batches of 4,000
gallons. Standard quantities of 4,000 gallons of direct materials are
processed which cost $0.60 per gallon. Kerosene can be sold without further
processing for $0.80 per gallon. It can be processed further to yield
gasoline, which can be sold for $1.25 per gallon. Gasoline requires
additional processing costs of $650 per batch, and 20% of the gallons of
kerosene will evaporate during production. Should we sell or process
further?
Created by: M. Mari
Fall 2007
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ACG 2071
Module 11: Differential Analysis and Product Pricing
Kerosene
Sales: 4,000g x $0.80
Costs of production:
4,000g x $0.60
Revenue from sales of kerosene
Gasoline
Sales: 3,200g* x $1.25
Cost of production:
Kerosene
Gasoline
Total costs of production
Revenue from sales of gasoline
$3,600
$2,400
$800
$4,000
$2,400
$ 650
$3,050
$950
Since the revenue from sales of kerosene are less than revenue from sale of
gasoline, then gasoline will be produced.
6. Accept Businesses at a Special Price
 Differential analysis is also useful in deciding whether to accept
additional business at a special price.
 The differential revenue that would be provided from the additional
business is compared to the differential costs of producing and
delivering the product to the customer.
 If the company is operating at full capacity, any additional production
will increase both fixed costs and variable.
 However, the normal production of the company is below full
capacity, additional business may be undertaken without increasing
fixed production costs.
 Only view variable costs
Example 11: Assume that the monthly capacity is 12,500 units. Current
sales and production are 10,000 units. The current manufacturing costs of
$20 per unit with fixed costs of $7.50. The normal selling price of the
product is $30. The manufacturer receives from an exporter an offer for
Created by: M. Mari
Fall 2007
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ACG 2071
Module 11: Differential Analysis and Product Pricing
5,000 units at $18 per unit. The production can be spread over three months.
Should we accept the special offer?
Do we have unused capacity?
Yes, capacity is 12,500 units and we are producing 10,000 units. So we
can produce an additional 2,500 units per month. The order is 5,000 units
over 3 months and that is feasible.
Costs of production
Less fixed costs
Variable costs of production
Special offer
Revenue from special offer
$20.00
$7.50
$12.50
$18.00
$5.50
Since revenue from special offer is positive, we should take the offer.
Setting Normal Product Selling Prices
 Differential analysis may be useful in deciding to lower selling prices
for special short run decisions, such as whether to accept business at a
price lower than the normal price.
 The normal selling price must be set high enough to cover all costs
and expenses and provide a reasonable profit.
 The normal selling price can be viewed as the targeted selling price to
be achieved in the long run.
 The basic approaches to setting this price as follows:
Market Methods
Demand based
Competition based
Cost plus Methods
Total cost concept
Product cost concept
Variable cost concept
 Managers using the market methods refer to the external market to
determine the price.
Created by: M. Mari
Fall 2007
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ACG 2071
Module 11: Differential Analysis and Product Pricing
 Demand based methods set the price according to the demand for the
product.
 If there is high demand for the product, then the price may be set high,
while the lower demand may require the price to be set low.
 Managers using the cost plus methods price the product in order to
achieve a target profit.
 Managers add to the cost an amount called MARKUP.
Total Cost Concept
All the costs of manufacturing a product plus the selling and administrative
expenses are included in the cost amount to which the markup is added.
Steps:
1. Determine the total cost of manufacturing the product.
a. Includes the direct materials, direct labor, and factory overhead
b. Includes the selling and administrative expenses
2. Cost per unit is then computed by dividing the total costs by the total
units expected to be produced and sold.
3. Markup percentage = Desired profit
Total cost
4. Selling price = Cost per unit + ( markup percentage X cost per
unit)
Example 13: The desired profit is $160,000.
Variable costs 100,000 units
Direct materials
Direct labor
Factory overhead
Selling and administrative expenses
Total variable costs
Fixed costs
Created by: M. Mari
Fall 2007
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Total Cost
$300,000
$1,000,000
$150,000
$150,000
$1,600,000
Unit Cost
$3.00
$10.00
$1.50
$1.50
$16.00
ACG 2071
Module 11: Differential Analysis and Product Pricing
Factory overhead
Selling and administrative
Total Fixed costs
$50,000
$20,000
$70,000
Steps:
1. Determine the total cost of manufacturing the product.
a. Includes the direct materials, direct labor, and factory overhead
b. Includes the selling and administrative expenses
Cost of manufacturing the product = Fixed costs + Variable Costs
Variable costs = $16.00 x 1,000,000 units = $1,600,000
Fixed costs = $20,000 + $50,000 = $70,000
Total cost = $1,600,000 + $70,000 = $1,670,000
2. Cost per unit is then computed by dividing the total costs by the total
units expected to be produced and sold.
Cost per unit = Total Cost
Total units
= $1,670,000
100,000
= $16.70 per unit
3. Markup percentage = Desired profit
Total cost
Markup Percentage = $160,000
$1,670,000
= 9.6%
4. Selling price = Cost per unit + ( markup percentage X cost per
unit)
Created by: M. Mari
Fall 2007
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ACG 2071
Module 11: Differential Analysis and Product Pricing
= $16.70 + ($16.70 X 9.6%)
= $18.30
Product Cost Concept
Only the cost of manufacturing the product termed the product cost, are
included in the cost amount to which the markup is added.
Estimated selling expenses, administrative expenses, and profits are included
in the markup.
Steps:
1. Determine the total cost of manufacturing the product include direct
materials, direct labor, and factory overhead.
2. Cost per unit is total cost manufacturing divided by the total units.
3. Markup % = Desired profit + Total selling & Administrative Expenses
Total Manufacturing Costs
4. Selling price = Cost per unit + (Cost per unit X Markup %)
Example 15 The desired profit is $160,000 with production of 100,000
units.
Variable costs 100,000 units
Direct materials
Direct labor
Factory overhead
Selling and administrative expenses
Total variable costs
Fixed costs
Created by: M. Mari
Fall 2007
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Total Cost
$300,000
$1,000,000
$150,000
$150,000
$1,600,000
Unit Cost
$3.00
$10.00
$1.50
$1.50
$16.00
ACG 2071
Module 11: Differential Analysis and Product Pricing
Factory overhead
Selling and administrative
Total Fixed costs
$50,000
$20,000
$70,000
Steps:
4. Determine the total cost of manufacturing the product.
a. Includes the direct materials, direct labor, and factory overhead
Cost of manufacturing the product = Fixed costs + Variable Costs
Variable costs = $14.50 x 1,000,000 units = $1,450,000
Fixed costs = $50,000
Total cost = $1,450,000 + $50,000 = $1,500,000
5. Cost per unit is then computed by dividing the total costs by the total
units expected to be produced and sold.
Cost per unit = Total Cost
Total units
= $1,500,000
100,000
= $15.00 per unit
6. Markup percentage
= Desired profit + Total selling & administrative expenses
Total cost
Markup Percentage = $160,000 + $150,000 + $20,000
$1,500,000
= 22%
4. Selling price = Cost per unit + ( markup percentage X cost per
unit)
= $15.00 + ($15.00 X 22%)
Created by: M. Mari
Fall 2007
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ACG 2071
Module 11: Differential Analysis and Product Pricing
= $15.00 + $3.30
= $18.30
Variable Cost Concept
 Emphasizes the distinction between variable and fixed costs in
product pricing.
 Only variable costs are included in the cost amount to which the
markup is added
Steps:
5. Determine the total cost of manufacturing the product include direct
materials, direct labor, variable selling and administrative expenses,
and variable factory overhead.
6. Cost per unit is total cost manufacturing divided by the total units.
7. Markup % = Desired profit + Total Fixed Costs
Total Variable Costs
8. Selling price = Cost per unit + (Cost per unit X Markup %)
Example 15 The desired profit is $160,000 with production of 100,000
units.
Variable costs 100,000 units
Direct materials
Direct labor
Factory overhead
Selling and administrative expenses
Total variable costs
Fixed costs
Factory overhead
Created by: M. Mari
Fall 2007
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Total Cost
$300,000
$1,000,000
$150,000
$150,000
$1,600,000
Unit Cost
$3.00
$10.00
$1.50
$1.50
$16.00
$50,000
ACG 2071
Module 11: Differential Analysis and Product Pricing
Selling and administrative
Total Fixed costs
$20,000
$70,000
Steps:
7. Determine the total cost of manufacturing the product.
a. Includes the direct materials, direct labor, and factory overhead
Cost of manufacturing the product = Fixed costs
Variable costs = $13.00 x 1,000,000 units = $1,300,000
Variable factory overhead = $1,50 x 100,000 = $150,000
Variable selling and administrative = $1,50 x 100,000 = $150,000
Total cost = $1,300,000 + $150,000 + $150,000 = $1,600,000
8. Cost per unit is then computed by dividing the total costs by the total
units expected to be produced and sold.
Cost per unit = Total Cost
Total units
= $1,600,000
100,000
= $16.00 per unit
9. Markup percentage
= Desired profit + Total fixed costs
Total variable cost
Markup Percentage = $160,000 + $50,000 + $20,000
$1,600,000
= 14.4%
4. Selling price = Cost per unit + ( markup percentage X cost per
unit)
= $16.00 + ($16.00 X 14.4%)
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Fall 2007
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ACG 2071
Module 11: Differential Analysis and Product Pricing
= $16.00 + $2.30
= $18.30
Created by: M. Mari
Fall 2007
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